Solve (x+1)(x+2)=2-x

$$( x + 1 ) ( x + 2 ) = 2 - x$$

Solve for x

$$x=-4$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$x^{2}+3x+2=2-x$$

Subtract 2 from both sides.

$$x^{2}+3x+2-2=-x$$

Subtract 2 from 2 to get 0.

$$x^{2}+3x=-x$$

Add x to both sides.

$$x^{2}+3x+x=0$$

Combine 3x and x to get 4x.

$$x^{2}+4x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}}}{2}$$

Take the square root of 4^{2}.

$$x=\frac{-4±4}{2}$$

Now solve the equation x=\frac{-4±4}{2} when ± is plus. Add -4 to 4.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-4±4}{2} when ± is minus. Subtract 4 from -4.

$$x=-\frac{8}{2}$$

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=0 x=-4$$

Steps for Completing the Square

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$x^{2}+3x+2=2-x$$

Add x to both sides.

$$x^{2}+3x+2+x=2$$

Combine 3x and x to get 4x.

$$x^{2}+4x+2=2$$

Subtract 2 from both sides.

$$x^{2}+4x=2-2$$

Subtract 2 from 2 to get 0.

$$x^{2}+4x=0$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+4x+2^{2}=2^{2}$$

Square 2.

$$x^{2}+4x+4=4$$

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{4}$$

Simplify.

$$x+2=2 x+2=-2$$

Subtract 2 from both sides of the equation.

$$x=0 x=-4$$